Bridge Table Calculations

DIVISIBLE/NON-DIVISIBLE

This section is designed to provide background and detailed information used to determine the distribution of weight on structures. It is not just the structures we are looking at but also the road itself.

WHY THE FORMULA IS NECESSARY

Bridges on Interstate System highways are used by a wide variety of traffic. They are designed to support expected loadings. However, as trucks grew heavier in the 1950s and 1960s, something had to be done to protect bridges. The solution was to tie allowable weights to the number and spacing of axles.

Axle spacing is as important as axle weight in bridge design. A bridge is analogous to thin ice on a pond. Walking on the ice concentrates a person's weight on the small area covered by the individual's feet, and then the ice may break. Lying down, however, spreads the same weight over a much larger area, and the ice is less likely to break. Consider trucks crossing a bridge:

In Figure 1 (A), the stress on bridge members as the longer truck rolls across is much less than that caused by the short vehicle in Figure 1 (B), even though both trucks have the same total weight and individual axle weights. The weight of the longer vehicle is spread out, while the shorter vehicle has all of the weight concentrated on a small area. The Federal-Aid Highway Amendments of 1974 increased the weights allowed on the Interstate system to 20,000 pounds on a single axle, 34,000 pounds on a tandem axle, and 80,000 pounds gross weight (23 U.S.C. 127). But Congress balanced this concession to productivity by enacting the Bridge Formula {500[(LN/N-1) +12N+36]}. The result is that motor vehicles may be loaded to the maximum weight only if each group of axles on the vehicle and their spacing also satisfy the requirements of the Formula. This prevents the vehicle from overstressing bridges in the same way that a person lying down on thin ice would minimize the risk of breaking through

W = the maximum weight in pounds that can be carried on a group of two or more axles to the nearest 500 pounds.

L = the distance in feet between the outer axles of any two or more consecutive axles.

N = the number of axles being considered.

Note: When the distance in feet includes a fraction of a foot of one inch or more the next larger number of feet shall be used. This only applies to Divisible Loads.

The formula limits the weight on groups of axles in order to reduce the risk of damage to highway bridges. Allowable weight depends on the number of axles a vehicle has and the distance between those axles. However, the single-or-tandem-axle weight limits supersede the Bridge Formula limits for all axles not more than 96 inches apart.

Until 1982, Federal law set only upper limits (or ceilings) on Interstate System weight limits. A few states retained significantly lower weight limits, which eventually became barriers to long-distance truck traffic. In 1982, Federal law was amended to make Interstate Systems weights limits, including the bridge formula limits, both the maximum and the minimum weights (i.e., floors and ceilings) that states must allow on the Interstate System.

How the Formula Is Used

To use the formula, {W=500[(LN/N-1) + 12N + 36]}, you take the number of axles and plug them in for N and the distance measured rounded to the next foot for L. The calculation would then go in the following order:

Everything within the parenthesis first

So you would take the length and multiply it by the number of axles being measured and divide that answer by the answer of the number of axles minus 1. So if you had a length of 36’ and Number of axles equaled 5. It would look like this. (36 X 5 / 5-1) then you reduce it to (180 divided by 4) and this would equal 45.

Multiple 12 by the number of axles (5), we would get 60.

So our formula now looks like this: W = 500[45 + 60 + 36]

We would add all the additions on the inside of the bracket like this: W = 500[141]

Now we multiply 141 by 500 and this gives us: W = 70,500 lbs

When calculating the formula by hand you would round the measurement after adding all the other measurements together. For instance if I had the following measurements of 13’, 4’4”,14’, 4’6” they would give me a measurement of 35’ 10”

So this means that on a bridge measurement of 36 ft with 5 axles the total allowed weight is 70,500 lbs.

Gross Weight

The weight of a vehicle or vehicle combination and any load thereon. The federal gross weight limit on the Interstate System is 80,000 pounds.

Single-Axle Weight

The total weight on one or more axles whose centers are not more than 40 inches apart. The federal single-axle weight limit on the Interstate System is 20,000 pounds.

Tandem-axle Weight

The total weight on two or more consecutive axles more than 40 inches but not more than 96 inches apart. The Federal tandem axle weight limit on the Interstate System is 34,000 pounds.

Interstate System weight limits in some States may be higher than these figures due to "grandfather" rights. When the Interstate System axle and gross weight limits were adopted in 1956, states were allowed to keep or "grandfather" those, which were higher. In 1975, states were allowed to keep or "grandfather" those, axle, gross and bridge formula limits which were higher than those that were established for the intersate system.

Bridge Formula calculations yield a series of weights HYPERLINK BRIDGE. However, the single axle weight limit replaces the Bridge Formula weight limit on axles not more than 40 inches apart, and the tandem-axle weight limit replaces the Bridge Formula weight limit for axles over 40 but not more than 96 inches apart. At 97 inches apart, two axles can carry 39,000 pounds and three axles 42,500 pounds, as shown in Figure 2.Federal law provided that any two or more consecutive axles may not exceed the weight computed by the Formula even though single axles, tandem axles, and gross weight are within legal limits. In other words, the axle group that includes the entire truck--sometimes called the "outer bridge" group--must comply with the Bridge Formula. But interior combinations of axles, such as the "tractor bridge" (axles 1, 2, and 3) and "trailer bridge" (axles 2, 3, 4, and 5), must also be in compliance with weights computed by the Formula (Figure 3).The most common vehicle checked for compliance with weight limit requirements is shown in Figure 3. While the Bridge Formula applies to each combination of two or more axles, experience shows that axle combinations 1 through 3, 1 through 5, and 2 through 5 are critical and must be checked. If these combinations are found to be satisfactory, all of the others on this type of vehicle will normally be satisfactory. The vehicle with weights and axle dimensions as shown in Figure 4 will be used to illustrate a Bridge Formula check.Before checking a vehicle for compliance with the Bridge Formula, its single-axle, tandem axle, and gross weight should be checked. Here the single axle (number 1) does not exceed 20,000 pounds, tandems 2-3 and 4-5 do not exceed 34,000 pounds each, and the gross weight does not exceed 80,000 pounds. These preliminary requirements are thus satisfied. The first Bridge Formula combination is checked as follows:Check axle of 1 thru 3 (Figure 5)Actual weight = 12,000 + 17,000 + 17,000 =46,000 poundsN = 3 axlesL = 20 feetW maximum = 51,000 lbs., which is more than the actual weight of 46,000 lbs., so the Bridge Formula requirement is satisfied.

Example--from The Bridge Table

This same number (51,000 pounds) could have been obtained from the Bridge Table by reading down the left side to L = 20 and across to the right where N = 3.

Federal law (23 U.S.C. 127) includes one exception to the Bridge Formula and the Bridge Table--two consecutive sets of tandem axles may carry 34,000 pounds each if the over-all distance between the first and last axles of these tandems is 36 feet or more. For example, a five-axle tractor-semitrailer combination may carry 34,000 pounds both on the tractor tandem (axles 2 and 3) and the trailer tandem (axles 4 and 5), provided axles 2 and 5 are spaced at least 36 feet apart. Without this exception, the Bridge Formula would allow an actual weight of only 66,000 to 67,500 pounds on tandems spaced 36 to 38 feet apart.

The procedure described above can be used to check any axle combinations, but several closely spaced axles usually produce the most critical situation.This vehicle has all legal axle weights but is still in violation. Axles 2-4 (Group 2) a (tridem) has a 9-foot spread measured from center of axle to center of axle, and is weighing 45,000 lbs. in figure 8. If you use the bridge chart for a 3-axle group at a 9-foot spread the tridem can only weigh 42,500 lbs. The vehicle would be over bridge on axles 2-4 (Group 2) by 2,500 lbs.Note: This is a violation. The load would have to be reduced, axles added, or spacing increased, to comply with the Bridge Formula

Federal Divisible Chart

Caution: This information paraphrases the actual provision in 23 U.S.C. 127 and 23 CFR 658 for the sake of clarity. In case of a dispute, the statue and regulations will govern.

steering axle needs to be stressed.

The inner bridges are where the majority of all weight is going to be carried.

A tractor may have a long wheelbase so the “outer” or overall bridge may be met, however, if the axle spacing on the trailer and/or trailers (inner bridge) is measured it may not allow the maximum outer bridge.

Based on the outer bridge the combination can carry 113,500 Lbs however, the inner bridge is allowed 96,000 meaning that the steer axle would have to carry 17,500 Lbs to get maximum bridge.

Allowed steering axle weight is determined by the amount shown on the tire(s) sidewalls (single rating on steer and VLS) are rated or a maximum weight of 20,000 lbs whichever is less. Sometimes steer axles are rated for more than legal but the limit is 20,000. If one tire has a greater weight rating than the other, the lesser of the two rating (weakest link) will be used.

The example above shows 6,175 lbs. if both tires are the same, the allowed weight is 12,350 lbs. If one side is rated for 6,175 lbs and the other side is rated for 6,610 lbs the total rating would be 12,350 not 12,785.

Allowed weight for a variable load suspension or “tags” axles is the weight rating of the tires or pounds per inch, whichever is less.

Permitted loads

= 450 lbs per inch for tires less than 11 inches wide.= 500 lbs per inch for tires 11 inches wide or greater.

Non-permitted = 600 lbs per inch.

Note: Using the example above the 11 is the width of the so that would be multiplied by 500 lbs. equaling 5,500 lbs. or 11,000 lbs. if both tires or the same size.When the tire sidewall shows the size (metric) of 255. You would multiply that by .04 to determine the standard size, which would be 10.2”.

BRIDGE ROAD RESTRICTIONS

Bridges with rated capacities less than the maximum legal limit in Utah have gross weight restrictions posted. A highway authority may prohibit the operation of any vehicle or impose restrictions on the weight of a vehicle upon any highway under its jurisdiction. UCA 72-7-408

NON-DIVISBILE LOADS

Non-Divisible loads are given an extra allowance on weights over the Federal Divisible bridge calculations.

(Refer to 72-7-404 (4))

The bridge formula used to calculate weights allowed for non-divisible loads is:

W=1.47 {500[ LN/N-1+12N+36]}

The groups that are 9’ wide are given an extra 7.5 % over what an 8’ wide axle is allowed.

The groups that are 10’ wide are given an extra 15 % over what an 8’ wide axle is allowed.

Trunion axles are given and extra 10% allowance over what an 8’ wide axle is allowed.